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3 years ago

Solve for the variable k^2+9k=0

Mathematics

1 answer:

pshichka [43]3 years ago

3 0

Answer:

Step-by-step explanation: two solution found is -9 and 0 that is the right answer

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8.45 as a mixed number

Vlad [161]

A mixed number is a combination of a whole number and a fraction, so in this case we have 8 as the whole part and 0.45 as the fraction, 0.45 is equal to 45/100, and that fraction can be simplified as well, lets see:
8.45 = 8 45/100
= 8 9/20

4 0

3 years ago

Which expressions are equivalent to (2^2-9) (x + 3)?

mestny [16]

Answer:

$(x^2-3^2)(x+3)$

$(x-3)(x+3)(x+3)$

$(x-3)(x+3)^2$

Step-by-step explanation:

Given

$(x^2-9)(x+3)$

Required

Select 3 equivalent expressions

$(x^2-9)(x+3)$

Express 9 as 3^2

$(x^2-3^2)(x+3)$ --- This is one equivalent expression

Take $x^2 - 3^2$ as difference of two squares

$(x-3)(x+3)(x+3)$ -- This is another equivalent expression:

Solving further:

$(x-3)(x+3)(x+3)$ becomes

$(x-3)(x+3)^2$ -- This is another equivalent expression:

Hence, the equivalent expressions are:

$(x^2-3^2)(x+3)$

$(x-3)(x+3)(x+3)$

$(x-3)(x+3)^2$

7 0

3 years ago

Solve by factoring <br>7x^2-14x=0

Nataly_w [17]

7x²-14x=0
7x²=-14x
sry idk the rest hope this helped a little bit

5 0

3 years ago

What are the coordinates of B

Citrus2011 [14]

Answer:

The coordinates of B is (-5, 4).

7 0

3 years ago

) The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday

Vsevolod [243]

Answer:

a) The standard deviation of this sampling distribution is 2.07.

b) The missing number is 4.14.

c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

$\mu = 272, n = 840, \sigma = 60$

(a) If we take many samples, the sample mean x⎯⎯⎯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?

Using the Central Limit Theorem:

$s = \frac{\sigma}{\sqrt{n}} = \frac{60}{\sqrt{840}} = 2.07$

The standard deviation of this sampling distribution is 2.07.

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?

Within 2 standard deviations of the mean.

So, 2*2.07 = 4.14

The missing number is 4.14.

(c) What is the 95% confidence interval for the population mean score μ based on this one sample?

Within 4.14 of the mean

272 - 4.14 = 267.86

272 + 4.14 = 276.14

The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

6 0

3 years ago